Basis Functions of Three-Dimensional Models for Compression, Transformation and Streaming

1. A method for streaming, over a network connection between a source and a destination, an animated digital display including a plurality of digital image frames, each digital image frame containing an animated object having a plurality of vertices, each of the plurality of vertices having a corresponding spatial coordinate, the method comprising the steps of: combining the set of vertices for the object contained in each of the plurality of digital image frames into a vertices data matrix, A; performing a singular value decomposition (SVD) on the vertices data matrix, wherein A U* W* V T ; determining the SVD basis matrix; sending the SVD basis matrix from the source to the destination via the network connection; determining a plurality of SVD coefficients; storing the SVD basis matrix at the destination; sending the plurality of SVD coefficients from the source to the destination via the network connection; and reconstructing the vertices data matrix as a function of the SVD coefficients and the SVD basis matrix.

2. The method of claim 1 , wherein the step of determining the SVD basis matrix includes the calculation of W* V T .

3. The method of claim 1 , wherein the step of determining the plurality of SVD coefficients, U, includes the calculation U A* V* W 1 .

4. The method of claim 3 , wherein the step of reconstructing the vertices data matrix includes the calculation U* W* V T .

5. The method of claim 1 , further including prior to the step of determining the SVD basis matrix the steps of: reducing the number of entries in the W matrix according to a predetermined threshold; and removing the corresponding rows in the V matrix.

6. The method of claim 1 , further including prior to the performing a singular value decomposition step the steps of: determining the rotation angles from the rotation data; determining the translation data; removing rotation data of the animated object from the vertices data matrix; removing translation data of the animated object from the vertices data matrix; forming a rotation-translation matrix, R, including the rotation angle and the translation data of the rotation data and translation data; transmitting the rotation-translation matrix, R, from the source to the destination via the network connection; and storing the rotation-translation matrix, R, at the source, wherein the step of reconstructing the vertices data matrix includes the step of multiplying the rotation-translation matrix, R, by the reconstructed vertices data matrix, A i .

7. The method of claim 1 wherein the vertices data matrix, A, includes a plurality of column vectors, and wherein prior to the step of performing a SVD, calculating the mean, M 0 , for each the plurality of column vectors, and removing the mean, M 0 , of each of the column vectors from each entry in the corresponding column vector, and wherein the step of reconstructing the vertices data matrix, A, further includes reconstructing the vertices data matrix as a function of the SVD coefficients, the SVD basis matrix, and the mean of each of the plurality of column vectors, M 0 .

8. The method of claim 7 , wherein the step of reconstructing the vertices data matrix includes the calculation U* W* V T M 0 .

9. The method of claim 7 , wherein the step of reconstructing the vertices data matrix is a function of the SVD coefficients, the SVD basis matrix, the mean of each of the plurality of column vectors, M 0 , and the rotation-translation matrix R.

10. The method of claim 7 , further including wherein the step of reconstructing the vertices data matrix includes the calculation R* (U* W V T M 0 ).

11. The method of claim 1 , prior to the step of reconstructing further including the steps: storing the matrix, U, at the destination; and transmitting from the source to the destination via the network, a plurality of weighting functions each corresponding to one or more rows the matrix U; retrieving the corresponding rows from the matrix U; weighting the one or more rows of the matrix U by the corresponding weighting function, and combining the weighted rows of the matrix U together.

12. A method for filtering an animated digital display including a plurality of digital image frames, each digital image containing an animated object having a plurality of vertices, each of the plurality of vertices having a corresponding spatial coordinate, the method comprising the steps of: combining the set of vertices for the object contained in each of the plurality of digital image frames into a vertices data matrix, A; performing a singular value decomposition (SVD) on the vertices data matrix, A, wherein A U* W* V T ; reducing the number of entries in the W matrix according to a predetermined threshold; and removing the corresponding rows in the V matrix.

13. A method for compressing an animated digital display including a plurality of digital image frames, each digital image frame containing an animated object having a plurality of vertices, each of the plurality of vertices having a corresponding spatial coordinate, the method comprising the steps of: combining the set of vertices for the object contained in each of the plurality of digital image frames into a vertices data matrix, A; performing a singular value decomposition (SVD) on the vertices data matrix, wherein A U* W* V T ; determining the SVD basis matrix, W* V T ; storing the SVD basis matrix; determining a plurality of SVD coefficients, U, wherein U A* V* W 1 ; storing the plurality of SVD coefficients; and reconstructing the vertices data matrix, A, as a function of the SVD coefficients and the SVD basis matrix, wherein A U* W* V T .

14. A computer programming product including a computer readable medium, said computer readable medium having a computer program stored thereon, said computer program for execution within a image processing unit for streaming, over a network connection between a source and a destination, an animated digital display including a plurality of digital image frames, each digital image frame containing an animated object having a plurality of vertices, each of the plurality of vertices having a corresponding spatial coordinate, said computer program comprising: program code for combining the set of vertices for the object contained in each of the plurality of digital image frames into a vertices data matrix, A; program code for performing a singular value decomposition (SVD) on the vertices data matrix, wherein A U* W* V T ; program code for determining the SVD basis matrix; program code for sending the SVD basis matrix from the source to the destination via the network connection; program code for determining a plurality of SVD coefficients; program code for storing the SVD basis matrix at the destination; program code for sending the plurality of SVD coefficients from the source to the destination via the network connection; and program code for reconstructing the vertices data matrix as a function of the SVD coefficients and the SVD basis matrix.

15. An apparatus for streaming, over a network connection between a source and a destination each having a source and destination network interface respectively, an animated digital display including a plurality of digital image frames, each digital image frame containing an animated object having a plurality of vertices, each of the plurality of vertices having a corresponding spatial coordinate, the apparatus comprising: a vertices data module, receiving the plurality of spatial coordinates corresponding to the plurality of vertices, the vertices data module configured and arranged to form a vertices-data-matrix, A; an SVD module receiving the vertices-data-matrix, A, and configured and arranged to perform a singular value decomposition (SVD) of the vertices-data-matrix, A, wherein A UWV T , the SVD module further configured and arranged to form the product WV T , and further configured and arranged to form a row vector of U according to U AVW 1 ; the source network interface receiving the product WV T and is configured and arranged to transmit the product WV T over the data network, the source network interface also receiving the row vector of U and further configured and arranged to transmit the row vector of U over the data network; the destination network interface receiving the product WV T and the row vector of the matrix U; a memory module to store the product WV T ; and a image reconstruction module receiving the row vector of U and the product WV T and is configured and arranged to combine the row vector of U with product WV T to reconstruct the image stored in the row of matrix A, wherein A UWV T .

16. The apparatus of claim 15 further comprising: a rotation translation module receiving the vertices data matrix A and being configured and arranged to form a rotation and translation removal matrix R and R 1 , and further configured and arranged to remove at least one of a rotation, a translation, or both contained within the vertices data matrix A, and forming a vertices data matrix A , wherein A RA; the SVD module receiving the vertices-data-matrix, A , and configured and arranged to perform a singular value decomposition (SVD) of the vertices-data-matrix, A , wherein A UWV T , the SVD module further configured and arranged to form the product WV T , and further configured and arranged to form a row vector of U according to U A VW 1 ; the source network interface further receiving the matrix R 1 and transmitting said R 1 across the data network to the destination network interface; the memory module to store the matrix R 1 ; and the image reconstruction module further receiving the matrix R 1 and being configured and arranged to combine the row vector of U with product WV T and with the matrix R 1 to reconstruct the image stored in the matrix A, wherein A R 1 UWV T .

17. The apparatus of claim 15 wherein the vertices data module is further configured and arranged to compute the mean value of the vertices data matrix, M 0 , and to remove the mean value, M 0 , from each element in the vertices data matrix A; and wherein the source network interface transmits the mean value, M 0 , to the destination network interface via the data network; and and wherein the image reconstruction module to reconstruct the image stored in the row of matrix A, wherein A UWV T M 0 .

18. A method for streaming, over a network connection between a source and a destination, an animated digital display including a plurality of digital image frames, each digital image frame containing an animated object having a plurality of vertices, each of the plurality of vertices having a corresponding spatial coordinate, the method comprising the steps of: combining the set of vertices for the object contained in each of the plurality of digital image frames into a vertices data matrix, A; performing a singular value decomposition (SVD) on the vertices data matrix, wherein A U* W* V T ; determining the SVD basis matrix; providing the SVD basis matrix from the source to the destination; determining a plurality of SVD coefficients; storing the SVD basis matrix at the destination; providing the plurality of SVD coefficients from the source to the destination; and reconstructing the vertices data matrix as a function of the SVD coefficients and the SVD basis matrix.

19. The method of claim 18 , wherein the step of determining the SVD basis matrix includes the calculation of W* V T .

20. The method of claim 18 , wherein the step of determining the plurality of SVD coefficients, U, includes the calculation U A* V* W 1 .

21. The method of claim 20 , wherein the step of reconstructing the vertices data matrix includes the calculation U* W* V T .

22. The method of claim 18 , further including prior to the step of determining the SVD basis matrix the steps of: reducing the number of entries in the W matrix according to a predetermined threshold; and removing the corresponding rows in the V matrix.

23. The method of claim 18 , further including prior to the performing a singular value decomposition step the steps of: determining the rotation angles from the rotation data; determining the translation data; removing rotation data of the animated object from the vertices data matrix; removing translation data of the animated object from the vertices data matrix; forming a rotation-translation matrix, R, including the rotation angle and the translation data of the rotation data and translation data; providing the rotation-translation matrix, R, from the source to the destination; and storing the rotation-translation matrix, R, at the source, wherein the step of reconstructing the vertices data matrix includes the step of multiplying the rotation-translation matrix, R, by the reconstructed vertices data matrix, A i .

24. The method of claim 18 wherein the vertices data matrix, A, includes a plurality of column vectors, and wherein prior to the step of performing a SVD, calculating the mean, M 0 , for each the matrix A, and removing the mean, M 0 , from each entry in the matrix A, and wherein the step of reconstructing the vertices data matrix, A, further includes reconstructing the vertices data matrix as a function of the SVD coefficients, the SVD basis matrix, and the mean of each of the plurality of column vectors, M 0 .

25. The method of claim 24 , wherein the step of reconstructing the vertices data matrix includes the calculation U* W* V T M 0 .

26. The method of claim 24 , wherein the step of reconstructing the vertices data matrix is a function of the SVD coefficients, the SVD basis matrix, the mean of each of the plurality of column vectors, M 0 , and the rotation-translation matrix R.

27. The method of claim 24 , further including wherein the step of reconstructing the vertices data matrix includes the calculation R (U* W* V T M 0 ).

28. The method of claim 18 wherein the step of providing the SVD basis matrix includes providing the SVD basis matrix on a computer readable medium.

29. The method of claim 23 wherein the step of providing matrix R, includes providing the matrix R on a computer readable medium.

30. A method for streaming, over a network connection between a source and a destination, an animated digital display including a plurality of digital image frames, the method comprising the steps of: calculating a set of vertices for the object contained in each of the plurality of digital images using a mathematical model of the object; combining the set of vertices for the object contained in each of the plurality of digital image frames into a vertices data matrix, A; performing a singular value decomposition (SVD) on the vertices data matrix, wherein A U* W* V T ; determining the SVD basis matrix; sending the SVD basis matrix from the source to the destination via the network connection; determining a plurality of SVD coefficients; storing the SVD basis matrix at the destination; sending the plurality of SVD coefficients from the source to the destination via the network connection; and reconstructing the vertices data matrix as a function of the SVD coefficients and the SVD basis matrix.

31. A method for streaming, over a network connection between a source and a destination, an animated digital display including a plurality of digital image frames, the method comprising the steps of: calculating a set of SVD coefficients for the object contained in each of the plurality of digital images using a mathematical model of the object; determining the SVD basis matrix; sending the SVD basis matrix from the source to the destination via the network connection; determining a plurality of SVD coefficients; storing the SVD basis matrix at the destination; sending the plurality of SVD coefficients from the source to the destination via the network connection; and reconstructing the vertices data matrix as a function of the SVD coefficients and the SVD basis matrix.

32. A method for displaying an animated digital display on a display device including a plurality of digital image frames, each digital image frame containing an animated object having a plurality of vertices, each of the plurality of vertices having a corresponding spatial coordinate, the method comprising the steps of: combining the set of vertices for the object contained in each of the plurality of digital image frames into a vertices data matrix, A; performing a singular value decomposition (SVD) on the vertices data matrix, wherein A U W V T ; determining the SVD basis matrix; providing the SVD basis matrix to the display device on a computer readable medium; determining a plurality of SVD coefficients; providing the plurality of SVD coefficients on a computer readable medium; reconstructing the vertices data matrix, by the display device as a function of the provided SVD coefficients and the provided SVD basis matrix.